# If - 5,k, - 1 are in AP then the values of k is equal to:

$

A. - 5 \\

B. - 3 \\

C. - 1 \\

D.{\text{ }}3 \\

E.{\text{ 5}} \\

$

Answer

Verified

331.2k+ views

Hint- This question is solved by using the formula for ${n^{th}}$ term when a series is in AP.

Now,

Given that $ - 5,K, - 1$ are in AP.

And we have to find the value of $k$ .

Now we know the formula to find the ${n^{th}}$ of an AP

${a_n} = {a_1} + \left( {n - 1} \right)d$

Here ${a_n}$ is the ${n^{th}}$ term,

${a_1}$ is the first term,

$d$ is the common difference and

$n$ is the number of terms which are to be found.

Now,

${a_3} = {a_1} + \left( {n - 1} \right)d$

Here, ${a_3} = - 1$ , ${a_1} = - 5$, $n = 3$ and

$

d = k - \left( { - 5} \right) \\

= k + 5 \\

$

Putting the value of these we get,

$

- 1 = - 5 + \left( {3 - 1} \right)\left( {k + 5} \right) \\

{\text{or }} - 1 = - 5 + 2\left( {k + 5} \right) \\

{\text{or }} - 1 + 5 = 2k + 10 \\

{\text{or }}4 = 2k + 10 \\

{\text{or }}4 - 10 = 2k \\

{\text{or }} - 6 = 2k \\

{\text{or }}k = - 3 \\

$

Thus, the correct option is $\left( B \right)$.

Note- Whenever we face such types of questions the key concept is that we should know the formulas when a series is in AP. Like we did in this question here, we apply the formula for ${n^{th}}$ term and we find the solution.

Now,

Given that $ - 5,K, - 1$ are in AP.

And we have to find the value of $k$ .

Now we know the formula to find the ${n^{th}}$ of an AP

${a_n} = {a_1} + \left( {n - 1} \right)d$

Here ${a_n}$ is the ${n^{th}}$ term,

${a_1}$ is the first term,

$d$ is the common difference and

$n$ is the number of terms which are to be found.

Now,

${a_3} = {a_1} + \left( {n - 1} \right)d$

Here, ${a_3} = - 1$ , ${a_1} = - 5$, $n = 3$ and

$

d = k - \left( { - 5} \right) \\

= k + 5 \\

$

Putting the value of these we get,

$

- 1 = - 5 + \left( {3 - 1} \right)\left( {k + 5} \right) \\

{\text{or }} - 1 = - 5 + 2\left( {k + 5} \right) \\

{\text{or }} - 1 + 5 = 2k + 10 \\

{\text{or }}4 = 2k + 10 \\

{\text{or }}4 - 10 = 2k \\

{\text{or }} - 6 = 2k \\

{\text{or }}k = - 3 \\

$

Thus, the correct option is $\left( B \right)$.

Note- Whenever we face such types of questions the key concept is that we should know the formulas when a series is in AP. Like we did in this question here, we apply the formula for ${n^{th}}$ term and we find the solution.

Last updated date: 03rd Jun 2023

•

Total views: 331.2k

•

Views today: 7.87k

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Name the Largest and the Smallest Cell in the Human Body ?

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

Lysosomes are known as suicidal bags of cell why class 11 biology CBSE

Two balls are dropped from different heights at different class 11 physics CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main

A sample of an ideal gas is expanded from 1dm3 to 3dm3 class 11 chemistry CBSE